Anabelian geometry with etale homotopy types
Number Theory
2016-12-12 v2 Algebraic Geometry
Algebraic Topology
Abstract
Anabelian geometry with etale homotopy types generalizes in a natural way classical anabelian geometry with etale fundamental groups. We show that, both in the classical and the generalized sense, any point of a smooth variety over a field k which is finitely generated over Q has a fundamental system of (affine) anabelian Zariski-neighbourhoods. This was predicted by Grothendieck in his letter to Faltings.
Cite
@article{arxiv.1504.01068,
title = {Anabelian geometry with etale homotopy types},
author = {Alexander Schmidt and Jakob Stix},
journal= {arXiv preprint arXiv:1504.01068},
year = {2016}
}
Comments
33 pages, refereed version